Equilibrium and Price Regulations
In their 1992 article (Production Subsidy and Countervailing Duties in Vertically Related Markets: The Hog-Pork Case Between
Canada and the USA, American Journal of Agricultural Economics 74(4), 48-49.) Moschini and Meilke estimated demand
function for hog as Qd = 53 – 20P + 20PB + 3PP + 2Y, where P, PB and PP are prices of hog, beef and poultry. Y is per
capita income. Supply function was found to be Qs = 78 + 40P – 60PHF , where PHF is price of hog feed.
1) Find equilibrium price Pe and equilibrium quantity Qe of hog if PB = 4, PP = 31/3, PHF = 1.5 and Y = 12.5K
.
Qd = 53 – 20P + 20PB + 3PP + 2Y = 168 – 20P = 40P – 12 = 78 + 40P – 60PHF = Qs
=>
Pe = 3 and Qe = 108
Alternatively use inverse demand and supply: Pd = 8.4 – 0.05Qd = 0.3 + 0.025Qs = Ps
=>
Pe = 3 and Qe = 108
2) Find social surplus SSe (sum of consumer surplus CSe & producer surplus PSe) with no price regulations
a. Consumer Surplus is area below demand and above price:
CSe = 108(8.4 – 3)/2
b. Producer Surplus is area above supply and below price:
PSe = 108(3 – 0.3)/2
SSe = CSe + PSe
.
= 291.6
= 145.8
= 437.4
3) Find new quantity exchanged Qc, full economic price Pfe, excess demand EDc (demand less supply), dead weight
loss DWLc, black market gain BMG, new producer surplus PSc & new consumer surplus CSc with price ceiling PC = 2.
a. Quantity exchanged is inverse supply at Pc:
Qc
= Qs|Pc = 40*2 – 12
= 68
b. Full Economic Price is inverse demand at Qc:
Pfe
= Ps|Qc = 8.4 – 0.05*68
= 5
c. Excess Demand is demand less supply at Pc:
EDc = 168 – 20*2 – (40*2 – 12)
= 60
d. Dead Weight Loss is area of triangle (Qc,Pfe), (Q,ePe), (Qc,Pc):
DWLc = (108 – 68)(5 – 2)/2
= 60
e. Black Market Gain is area of rectangle 0Qc and PcPfe:
BMG = 68*(5-2)
= 204
f. Producer Surplus at Pc:
PSc = 68*(2 – 0.3)/2
= 57.8
g. Consumer Surplus at Pc:
CSc = 68*(8.4 – 5)/2
= 115.6
PSc + CSs + DWLc + BMGc
= 437.4
4) Find new quantity exchanged Qf, excess supply ESf (supply less demand), government subsidy GSf, new consumer
surplus CSf, new dead weight loss DWLf and new producer surplus PSf with price floor PF = 4
.
a. Quantity exchanged is inverse demand at Pf:
Qf
= Qd|Pf = 168 – 20*4
= 88
b. Excess Supply is supply les demand at Pf:
ESf = (40*4 – 12) – 88
= 60
c. Government Subsidy is area of rectangle Esf and 0Pf:
GSf = 60*4
= 240
d. Consumer Surplus at Pf:
CSf = 88*(8.4 – 4)/2
= 193.6
e. DWL is area of triangle (Qf,Pf), (Q,ePe) and (Qf,Ps|Qf):
DWLf = (108 – 88)*[4 – (.3+.025*88)]/2
= 15
f. Producer Surplus at Pf is (Cse + Pse) – (CSf + DWL):
PSf = (291.6 + 145.8) – (193.6 + 15)
= 228.8
DWLf + CSf + PSf
(33.33% lower Pc is more destructive than 33.33% higher Pf: DWLc > DWLf)
= 437.4
5) Find new quantity exchanged Qt, buyer price Pbt, producer price Ppt, tax revenue TRt, new DWLt, new consumer
surplus CSt & new producer surplus PSt with excise ($ amount levied on pack of cigarettes or gallon of gas) tax t = 1.5 .
a. y intercept of Ps increases by t:
Pst
= 1.8 + 0.025Q = 8.4 – 0.05Q = Pd
=>
Qt
= 88
b. Buyer’s P is new equilibrium P:
Pbt
= Pd|Qt = 8.4 – 0.05*88
= 4
c. Producer’s P is Pbt less tax:
Ppt
= 4 – 1.5
= 2.5
d. Tax Revenue is area of rectangle:
TRt = tQt = 1.5*88
= 132
e. DWL is area of triangle:
DWLt = 1.5(108 – 88)/2
= 15
f. CS at t is:
CSt = 88(8.4 – 4)/2
= 193.6
g. PS at t is:
PSt = 88(2.5 – 0.3)/2
= 96.8
TRt + DWLt + CSt + PSt
= 437.4